To analyze these data, it is useful to consider separately the runs starting with different ranges of activity values. To this end, we show in Fig. REF  the distribution of activity \(a_0\)  values at the beginning of a run. The distribution is unimodal and gets wider with increasing \(n\) , which is consistent with earlier results known for steady state activity distribution [1]}, [2]}, [3]}. The distribution is also roughly symmetric about the peak. The mean value of \(a_0\)  (shown by a red filled circle in Fig. REF ), as well as the adapted level of activity (shown by an empty circle), lie close to the peak position. Therefore, the activity values near the peak can be considered to be in the medium range, the ones near the left (right) tail belong to low (high) range. In Fig. REF  of Appendix  we show the distribution of run durations which start with low, medium or high activity values. As expected, the long runs are least probable for high \(a_0\)  and most probable for low \(a_0\) . The integrated quantity, i.e. the number of runs persisting at least till time \(t\) , starting with \(a_0\)  values belonging to these three different ranges has been plotted in Fig. REF . As we show below, these variations play a crucial role in \(\Delta m^\pm (t)\)  behavior.
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